Pieces of animal skin eaten by old fatty (6)
I believe the answer is:
greasy
'fatty' is the definition.
(synonyms)
'pieces of animal skin eaten by old' is the wordplay.
'pieces of animal skin' becomes 'as' (I can't justify this - if you can you should believe this answer much more).
'eaten by' means one lot of letters goes inside another (inserted letters get eaten).
'old' becomes 'grey' (similar in meaning).
'as' placed into 'grey' is 'GREASY'.
Can you help me to learn more?
(Other definitions for greasy that I've seen before include "Unctuous or ingratiating" , "well-lubricated" , "Unctuous, being lubricated" , "Cheap 24" , "Covered with fat" .)